I did NOT say "the pressure is higher down near the primer" I said the powder starts to burn there, so the hot gas expands through the flash-hole quicker than through the neck at the other end of the case. Plus, the primer is obviously easier to push backwards, the reason fired .30-30 cases often show "high primers."
Just because the peak pressure is evenly distributed throughout the inside of the case doesn't mean pressure doesn't affect everything in the same way during the initial powder burn.
